In this case, theY axis would be called the axis of reflection. Math Definition: Reflection Over the Y AxisĪ reflection of a point, a line, or a figure in the Y axis involved reflecting the image over the Y axis to create a mirror image. In this case, the x axis would be called the axis of reflection. This means, all of the x -coordinates have been multiplied by -1. The preimage above has been reflected across he y -axis. This complete guide to reflecting over the x axis and reflecting over the y axis will provide a step-by-step tutorial on how to perform these translations.įirst, let’s start with a reflection geometry definition: Math Definition: Reflection Over the X AxisĪ reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. The most common lines of reflection are the x -axis, the y -axis, or the lines y x or y x. This idea of reflection correlating with a mirror image is similar in math. In real life, we think of a reflection as a mirror image, like when we look at own reflection in the mirror. Learning mathematics is growing neuron connections in one’s brain like in growing a garden, processes are not freely permutable, and, in many cases, cannot be reversed and done again.Learning how to perform a reflection of a point, a line, or a figure across the x axis or across the y axis is an important skill that every geometry math student must learn. By certain age, you start to understand, that there were things that you had to have done 20 years ago, not today or tomorrow.Īnother nasty property of time: you can re-use space (say, empty a cupboard and fill it again), but cannot re-use time.īoth of these principles apply to learning mathematics: certain things have to be mastered at a certain age, and in specific order. In real life, time is the principal source of non-permutability (or non-commutativity, in mathematical parlance) of events. These rotations and their consecutive execution are described as matrices (certain tables of numbers) and their multiplication (defined by some specific rules) – and, as a consequence, for multiplication of matrices, in most cases, the result depends on the order of multiplicands, \(xy \ne yx\). In geometry, the result of composition (that is, consecutive application) of rotations and other geometric transformations in the space almost always depends on the order in which they are performed. For triangle ABC with coordinate points A (3,3), B (2,1), and C (6,2), apply a reflection over the line yx. The line yx, when graphed on a graphing calculator, would appear as a straight line cutting through the origin with a slope of 1. You would perhaps agree that \(xy \ne yx\). In this video, you will learn how to do a reflection over the line y x. \(x\) is putting a sock on the left foot and \(y\) is putting a boot on the same foot.\(x\) is putting a sock on the left foot and \(y\) is putting a sock on the right foot very obviously, the order of operation does not matter, \(xy = yx\). A kindergarten level “real life” example: Let \(x\) and \(y\) be two processes or operations and \(xy\) is the outcome of their consecutive application: first \(x\), then \(y\). The expression \(xy\) can be used in a variety of situation for different kinds of mathematical objects (not only to numbers!) and operations on them, and in many (if not in most) situations \(xy\) is not equal \(yx\). My answer to a question on Quora: When exactly is xy not equal to yx?
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